In Figure REF  we illustrate that the quality of the automatic segmentation with few columns of \(W\)  strongly depends
on the capability of the selected metric to capture the features of the mesh. In this example we show that even if we compute
the whole affinity matrix \(W\) , the resulting automatic segmentation is far a way from the ground truth segmentation,
as it is shown by the values of \(d_R\)  and \(d_J\)  between these segmentations (\(d_R = 0.415\) , \(d_J = 0.742\) ). On the other
hand, the automatic segmentations obtained computing \(0.5\%\)  and \(100\%\)  of the columns of \(W\)  are very similar, since the
values of \(d_R\)  and \(d_J\)  between them are small (\(d_R=0.010\)  and \(d_J=0.064\) ). Hence, the segmentation with few columns
is also not good in comparison with the ground truth segmentation. Finally, in this example we also observe that the body
of fish is subdivided in clusters with similar areas. As other authors pointed out [1]}, this behavior is typical
of segmentations based on k-means algorithm.
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